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© 2020 Conscientia Beam. All Rights Reserved. 

COMPARATIVE ANALYSIS OF REFERENCE EVAPOTRANSPIRATION BY 
HARGREAVES AND BLANEY-CRIDDLE EQUATIONS IN SEMI-ARID CLIMATIC 
CONDITIONS   

 

 

 Muhammad 
Hafeez1+ 
Zia Ahmad Chatha2  
Alamgir Akhtar Khan3  
Allah Bakhsh 
Gulshan4 
Abdul Basit5    
Fatima Tahira6 

 

1Department of Agricultural Engineering, Faculty of Agricultural sciences 
and Technology, Bahauddin Zakariya University, Multan, Pakistan. 

 
2Department of Food Engineering, Faculty of Agricultural Engineering and 
Technology, University of Agriculture, Faisalabad, Pakistan. 

 
3Department of Agricultural Engineering, MNSUA, Multan, Pakistan. 

 
4,5Department of Botany, Ghazi University, Dera Ghazi Khan, Pakistan. 

 
6Department of Mathematics, Institute of Southern Punjab, Multan, 
Pakistan. 

 

 
(+ Corresponding author) 

 ABSTRACT 
 
Article History 
Received: 14 April 2020 
Revised: 25 May 2020 
Accepted: 22 September 2020 
Published: 19 October 2020  
 

Keywords 
ETo 
FAO-56 PM 
Blaney-Criddle 
Hargreaves 
Semi-arid 
Pakistan. 

 
There are various equations for calculation of reference evapotranspiration (ETo), but 
the Penman-Monteith (PM FAO-56) equation has been considered as the standard ETo 
equation. The key problem of PM FAO-56 equation is that it uses large number of 
weather parameters like air temperature, wind velocity, humidity and sun radiation as 
input. These weather parameters are not accessible at all weather stations of the world 
especially in developing countries. So, ablatives ETo equations like Hargreaves (HG) 
and Blaney-Criddle (BC) equations are used for estimation of ETo which required very 
small number of weather parameters that are readily available at most of the weather 
stations of the world. A research is conducted to compare HG and BC ETo equations 
for estimation of monthly ETo under semi-arid climatic regions of Lahore, Faisalabad 
and Peshawar, Pakistan. The PM FAO-56 ETo equation is considered as reference ETo 
equation for the assessment of HG ETo and BC ETo equation. The statistical results 
indicate that HG ETo equation overestimates PM FAO-56 ETo method by 7.91% at 
Lahore weather station, 5.59 % at Faisalabad weather station and 11.95% at Peshawar 
weather station. The BC ETo equation overestimates PM FAO-56 ETo equation by 
34.345% at Lahore weather station, 28.637% at Faisalabad weather station and 21.44% 
at Peshawar weather station. The variation of HG ETo equation with PM FAO-56 
ETo equation with RMSE of 0.487 mm/day at Lahore weather station, 0.521 mm/day 
at Faisalabad weather station and 0.985 at Peshawar weather station is noted.  The 
variation of BC ETo equation with PM FAO-56 ETo equation having RMSE of 3.03 at 
Lahore weather station, 2.58 at Faisalabad weather station and 1.96 at Peshawar 
weather station is noted.  
 

Contribution/Originality: The objectives of this study is to compare the HG ETo and BC) ETo equations 

against FAO-56 PM ETo equation in semi-arid climatic conditions. 

 

1. INTRODUCTION 

Pakistan is under the problem of water shortage and the demand of water for irrigation is also increased due to 

mounting demand of food and fiber [1]. Pakistan is in between the arid to semi-arid region [2]. The knowledge of 

Current Research in Agricultural Sciences 
2020 Vol. 7, No. 2, pp. 52-57. 
ISSN(e): 2312-6418 
ISSN(p): 2313-3716 
DOI: 10.18488/journal.68.2020.72.52.57 
© 2020 Conscientia Beam. All Rights Reserved. 

 
 
 

 
 
 

 

 
 
 
 

https://orcid.org/0000-0002-3262-7014
https://www.doi.org/10.18488/journal.68.2020.72.52.57


Current Research in Agricultural Sciences, 2020, 7(2): 52-57 

 

 
53 

© 2020 Conscientia Beam. All Rights Reserved. 

ETo is a key element for the management of water resources [3]. Numerous researchers have argued that 

Penmen–Monteith (FAO-56 PM) ETo method can be applied as a reference ETo method as compared to the other 

experimental ETo methods [4-7]. The PM ETo method requires large number of weather parameters i-e 

atmospheric temperature, relative humidity, solar radiation, wind velocity etc. But, availability of these weather 

parameters is not accessible at all the weather stations of the globe specially in developing country like Pakistan. 

Therefore, it appears reasonably to substitute it by other ETo methods which require small number of weather 

parameters [8]. The accuracy of a particular ETo method depends greatly on the climatic situations of the research 

area [9]. The objectives of this study are to compare the HG ETo and BC) ETo equations against FAO-56 PM 

ETo equation in semi-arid climatic conditions. 

 

2. MATERIALS AND METHODS 

2.1. Study Area 

The data of three meteorological weather stations Lahore, Faisalabad and Peshawar are used to estimate the 

reference evapotranspiration (ETo). The GPS (Global Positioning system) coordinates of Lahore are 31.33o N and 

74.20o E and height of 214 m from the ocean. Lahore sorts semi-dry climatic conditions. The GPS (Global 

Positioning System) coordinates of Faisalabad are 31.26o N and 73.08o E and elevation of 185.6 meters. The 

weather of Faisalabad sorts semi-arid climatic conditions with very warm and moist midsummers and arid cold 

wintertime. The GPS (Global Positioning System) coordinates of Peshawar are 34.02o N, 71.56o E and elevation of 

327 m from the sea. It has warm semi-arid weather conditions with very thirsty summers and slight winters-time. 

The mean monthly weather data period, climate conditions and Global Positioning System (GPS) of weather 

stations used in the study are given in Table 1. 

 
Table-1. Global Positioning System and climate of weather stations of study regions. 

Station Latitude Longitude Elevation (m) Data Period Climate 

Lahore 31.33o N 74.20o E 214.0 2000-2010 hot semi-arid 
Faisalabad 31.26o N 73.08o E 185.6 2001-2015 hot semi-arid 
Peshawar 34.02o N 71.56o E 327.0 2000-2009 hot semi-arid 

            

2.2. Reference Evapotranspiration (ETo) Methods 

2.2.1. FAO-56 Penman-Monteith ETo Method 

For estimation of ETo by FAO-56 PM equation Computer model [10] is used. The input data required are 

minimum and maximum air temperatures, relative humidity, wind velocity and sunshine hours. The following 

FAO-56 PM equation is suggested by  Majeed, et al. [10]. 

                                                          (1) 

Where, ETo is the reference evapotranspiration (mm d−1); Δ is the slope of the saturation vapor pressure 

function (kPa (°C)−1 );  Rn is the net radiation (MJ m−2 day−1); G is the soil heat flux density (MJ m−2 day−1); T is the 

mean air temperature (°C); U2 is the average 24-hour wind speed at 2-meter height (m s−1); (es-ea) is the vapor 

pressure deficit (kPa); and γ is the psychometric constant (kPa (°C)−1). The computation of all data required for the 

calculation of the ET0 followed the equation given by Allen, et al. [11]. 

 

2.3. Hargreaves ETo Equation 

ETo calculated by applying Hargreaves ETo equation suggested by Hargreaves and Samani [12]  is given as  

                    (2) 



Current Research in Agricultural Sciences, 2020, 7(2): 52-57 

 

 
54 

© 2020 Conscientia Beam. All Rights Reserved. 

Where, ETo HG is in mm day-1 and Tmean is mean air temperatures (0C). A coefficient of 0.408 is used to convert 

MJm-2 day -1 into mmd-1 suggested by Allen, et al. [11] and 0.0023 is the original coefficient of the Hargreaves ETo 

equation given by Hargreaves and Samani [13]. Due to the low data requirement, it is often applied under 

conditions where less data is available and especially, when only air temperature is available [14].  

 

2.4. Blaney-Criddle ETo Equation 

The original equation as described by Blaney and Criddle [1] is given as: 

 

Where, 

a =0.0043(RH min)-n/N-1.41,                                                                                             (4) 

b =0.82-0.0041(RH min) +1.07(n/N) + 0.066(u d) - 0.006(RH min) (n/N)-0.0006(RH min) (ud)              (5) 

With T being the mean monthly air temperature (°C) and p the monthly percentage of the annual daytime 

hours. 

 

2.5. Statistical Analysis 

The RMSE, PE and R2 are defined in Equations 6, 7 and 8. 

                                                         (6) 

                                                         (7) 

                                          (8) 

 

3. RESULTS AND DISCUSSION 

The Hargreaves (HG) ETo equation and Blaney-Criddle (BC) ETo equation compared with the standard 

Penman-Monteith (FAO-56 PM) ETo equation for monthly estimation of ETo in semi-arid climatic conditions of 

Lahore, Faisalabad and Peshawar, Pakistan. The Hargreaves (HG) ETo equation overestimated FAO-56 PM ETo 

equation by 7.91% at Lahore weather station as shown in Figure 1 and in Table 2. 

  

 
Figure-1. Monthly comparison of ETo_PM with HG at Lahore station. 

 
 



Current Research in Agricultural Sciences, 2020, 7(2): 52-57 

 

 
55 

© 2020 Conscientia Beam. All Rights Reserved. 

Table-2. Statistical analysis of HG and BC ETo Equations compared with FAO-56 PM ETo equation at Lahore station. 

Equation % Error RMSE R2  Mean SD 

Hargreaves 7.91 0.487 0.984  4.29 1.64 
Blaney-Criddle 34.345 3.03 0.8  6.02 4.04 

 

 

When the Blaney-Criddle ETo equation is compared with the standard FA0-56 PM ETo equation, it 

overestimated FAO-56 PM ETo equation by 34.34% at Lahore weather station as shown in Table 2 and Figure 2. 

 

 
Figure-2. Monthly comparison of ETo_PM with BC at Lahore station. 

 

The Hargreaves (HG) ETo equation is compared with standard Penman-Monteith (FAO-56 PM) ETo 

equation in semi-arid climatic conditions of Faisalabad. The HG ETo equation overestimates in winter and 

underestimates in summer by 5.59% when compared with FAO-56 PM ETo equation at Faisalabad as shown in 

Figure 3 and Table 3. The underestimation of ETo at Faisalabad weather station by Hargreaves (HG) ETo 

equation  over  FAO-56 PM ETo equation in summer is due to blowing of high speed wind in summer and 

underestimation is due blowing of low speed wind in winter. The Penman-Monteith (FAO-56 PM) ETo equation 

uses wind speed parameter in its execution but Hargreaves (HG) ETo equation does not use it that is why the 

FAO-56 PM ETo equation results more ETo values in summer and low ETo values in winter than HG ETo 

equation. The R2 between HG ETo equation and FAO-56 PM ETo equation is 0.98.  

 
Table-3. Statistical analysis of HG and BC ETo Equations compared with FAO-56 PM ETo equation at Faisalabad station. 

Equation % Error RMSE R2 Mean SD 

Hargreaves 5.59 0.521 0.98 4.64 1.76 
Blaney-Criddle 28.63 2.58 0.93 6.13 3.99 

 

 

 
Figure-3. Monthly comparison of ETo _ PM with HG at Faisalabad station. 

 

The BC ETo equation overestimates PM FAO-56 ETo equation by 28.637% at Faisalabad weather station 

when compared with FAO-56 PM ETo equation as shown in Figure 4 and Table 3.  



Current Research in Agricultural Sciences, 2020, 7(2): 52-57 

 

 
56 

© 2020 Conscientia Beam. All Rights Reserved. 

 
Figure-4. Monthly comparison of ETo _ PM with BC at Faisalabad station. 

 

The HG ETo equation overestimates the FAO-56 PM ETo equation in winter and underestimates in summer 

by 11.95% when compared with FAO-56 PM ETo equation at Peshawar weather station as shown in Figure 5 and 

Table 4. 

 

 
Figure-5. Monthly comparison of ETo _ PM with HG at Peshawar station. 

 
Table-4. Statistical analysis of HG and BC ETo Equations compared with FAO-56 PM ETo equation at Peshawar station. 

Equation % Error RMSE R2 Mean SD 

Hargreaves 11.95 0.985 0.98 4.29 1.79 
Blaney-Criddle 21.44 1.96 0.96 6.18 4.03 

 

 

The BC ETo equation overestimates FAO-56 PM ETo equation by 21.44% at Peshawar weather station of 

semi-arid climatic region as shown in Figure 6 and Table 4. 

 

 
Figure-6. Monthly comparison of ETo _ PM with BC at Peshawar station. 

 

4. CONCLUSION 

This study is conducted to assess the performance of Hargreaves (HG) and Blaney-Criddle (BC) ETo equations 

against standard Penman-Monteith (FAO-56 PM) ETo equation in semi-arid climatic regions of Lahore, Faisalabad 

and Peshawar. The comparison showed that Hargreaves (HG) ETo equation underestimates and overestimates 

FAO-56 PM ETo equation while Blaney-Criddle (BC) ETo equation overestimates the FAO-56 PM ETo equation 

in all the semi-arid climatic regions of Lahore, Faisalabad and Peshawar.  



Current Research in Agricultural Sciences, 2020, 7(2): 52-57 

 

 
57 

© 2020 Conscientia Beam. All Rights Reserved. 

Funding: This study received no specific financial support.    
Competing Interests: The authors declare that they have no competing interests.  
Acknowledgement: The authors would like to thank Pakistan Meteorological Department, 
Lahore and Peshawar for providing the climatic data records used in this research. 

 

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